There already exist several known sending/receiving systems comprising several transmitter antennas and using space-time codes. The earliest systems proposed all used orthogonal space-time block codes.
Thus, Alamouti in “A Simple Transmit Diversity Technique for Wireless Communications”, IEEE J. Sel. Areas Comm., 1998, 16, (8), pp. 1451-1458, presented the first system using a rate-one orthogonal space-time block code (where rate is defined as the ratio between the number N of symbols sent and the number L of symbol times or periods during which they are sent), for two transmitter antennas.
Tarokh et al. (“Space-time block codes from orthogonal designs”, IEEE Trans. on Information Theory, 1999, 45, (5), pp. 1456-1467) then generalized the orthogonal space-time block codes to systems comprising three or four transmitter antennas. However the rate values R=N/L obtained were only rate ½ or rate ¾.
The next studies led to envisaging the use of non-orthogonal space-time block codes. Thus Jafarkhani (“A Quasi-Orthogonal Space-Time Block Code”, IEEE Trans. Comm., 2001, 49, (1), pp 1-4) and Tirkonnen et al. (“Minimal non-orthogonality rate one space-time block code for 3+ Tx antennas”, ISSSTA, 2000, pp 429-432) have found rate-one non-orthogonal space-time block codes for a four-antenna system.
Subsequently, Damen et al. (“Diagonal Algebraic Space-Time Block Codes”, IEEE Trans. Inf. Theory, 2002, 48, (3), pp 628-626) envisaged the use of non-orthogonal space-time codes based on a Hadamard construction and other rotations with a number of transmitter antennas equal to the size of the code matrix.
Xin et al., in “Time Constellation-Rotating Codes Maximizing Diversity and Coding Gains”, GLOBECOM, San Antonio, 2001, pp 455-459, subsequently presented other rotation-based space-time codes.
One drawback of Alamouti's or Tarokh's orthogonal space-time codes is that they require the channels to be constant for the duration L, corresponding to the number of symbol periods during which the symbols are sent.
Such codes therefore place heavy constraints on the sending/receiving systems, and cannot be used to exploit the diversity of the channel.
One drawback of the non-orthogonal space-time codes proposed by Jafarkhani, Tirkonnen, Damen or Xin is that they require the channel to be constant for a period L=Nt, where Nt is the number of antennas at transmission. This is particularly true for the Damen and Xin codes.
In other words, a major drawback of all the space-time codes proposed in the literature is that they require the solution to be placed in the context of a quasi-static channel. This is particularly restrictive and does not permit the diversity of the channels to be exploited.
Furthermore, the Jafarkhani and Tirkonnen codes dictate a maximum likelihood (ML) decoding whose complexity increases exponentially with the order of modulation and the code size.
Finally, another drawback of the Damen algebraic space-time codes, which rely on a Hadamard construction, is that they have to be sent in a particular matrix form. They therefore cannot be used to obtain a choice of encoding that is flexible according to the variations of the channel.